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Debussy, Math, and the Golden Ratio

Given that Debussy’s music is apparently so concerned with mood and colour, one may be surprised to discover that, according to Howat, many of his greatest works appear to have been structured around mathematical models even while using an apparent classical structure such as sonata form. Howat suggests that some of Debussy’s pieces can be divided into sections that reflect the golden ratio, frequently by using the numbers of the standard Fibonacci sequence. Sometimes these divisions seem to follow the standard divisions of the overall structure. In other pieces they appear to mark out other significant features of the music. The 55 bar-long introduction to ‘Dialogue du vent et la mer’ in La mer, for example, breaks down into 5 sections of 21, 8, 8, 5 and 13 bars in length. The golden mean point of bar 34 in this structure is signalled by the introduction of the trombones, with the use of the main motif from all three movements used in the central section around that point.

The only evidence that Howat introduces to support his claim appears in changes Debussy made between finished manuscripts and the printed edition, with the changes invariably creating a Golden Mean proportion where previously none existed. Perhaps the starkest example of this comes with La cathédrale engloutie. Published editions lack the instruction to play bars 7–12 and 22–83 at twice the speed of the remainder, exactly as Debussy himself did on a piano-roll recording. When analysed with this alteration, the piece follows Golden Section proportions. At the same time, Howat admits that in many of Debussy’s works, he has been unable to find evidence of the Golden Section (notably in the late works) and that no extant manuscripts or sketches contain any evidence of calculations related to it.